1. Field of the Invention
The present invention generally relates to servomechanisms. In particular, this invention relates to methods and systems to attenuate the influence of internal and external disturbances in low-frequency range, e.g., friction, shock and vibration, so as to further improve system positioning accuracy and increase the robustness of the servomechanisms.
2. Description of the Related Art
Problem to be Solved
Precision servomechanisms are finding more and more widespread applications such as mass data storage, stages for various key semiconductor fabrication processes as in step and repeat micro-lithography, wafer dicing, probing and scanning probe microscopy. For a system with high positioning accuracy requirement, some disturbances previously neglected or simplified usually in control system design must be taken into account and reconsidered. The disturbance is defined here as anything which causes a control system to leave its control goal. The disturbances preventing the system accuracy of a servomechanism from further improvement, for example in a hard disk drive of mass data storage, are mainly: (1) internal system nonlinearities, e.g., ribbon flexibility, windage, and friction of the bearing structure supporting the actuator, and (2) external disturbances, e.g., shock and vibration.
Friction, which depends on many factors such as asperity of the contacted surfaces, situation of lubrication and temperature, has two different presentations: pre-sliding friction and sliding friction. (See, for example, B. Armstrong-Hélouvry, P. Dupont, and C. Canudas de Wit, “A survey of models, analysis tools and compensation methods for control of machines with friction,” Automatica, Vol. 30, No. 7, pp. 1083-1138, 1994.) In the pre-sliding stage, which is usually in the range of less than 10−5 m and dominated by the elasticity of the contacting asperity of surfaces, friction depends on both system position and velocity. Nonlinear dynamics such as hysteresis of friction to displacement and friction to velocity have been observed by many researchers. (See, for example, B. Armstrong-Hélouvry, P. Dupont, and C. Canudas de Wit, “A survey of models, analysis tools and compensation methods for control of machines with friction,” Automatica, Vol. 30, No. 7, pp. 1083-1138, 1994; D. Abramovitch, F. Wang, and G. Franklin, “Disk drive pivot nonlinearity modeling part I: frequency domain,” Proceedings of the America Control Conference. Baltimore, Md., June 1994, pp. 2600-2603; F. Wang, T. Hust, D. Abramovitch, and G. Franklin, “Disk drive pivot nonlinearity modeling part II: time domain,” Proceedings of the America Control Conference, Baltimore, Md., June 1994, pp. 2604-2607; K. Eddy and W. Messner, “Dynamics affecting tracking bias in hard disk drive rotary actuators,” Proceedings of the America Control Conference, Seattle, Wash., June 1995, pp. 1055-1060; and C. Canudas de Wit, H. Olsson, K. J. Astrom, and P. Lischinsky, “A new model for control of systems with friction,” IEEE Transactions on Automatic Control., Vol. 40, No. 3, pp. 419-425, 1995.) In the sliding stage, friction is dominated by the lubrication of the contacting surfaces and has the function of system damping. Friction in the sliding stage can usually be represented by various single variable functions of velocity.
The problem of friction in servomechanisms has long been observed and researched. (See, for example, B. Armstrong-Hélouvry, P. Dupont, and C. Canudas de Wit, “A survey of models, analysis tools and compensation methods for control of machines with friction,” Automatica, Vol. 30, No. 7, pp. 1083-1138, 1994.) Recently, this phenomenon receives much more attention due to the new challenges for high precision, for example, in hard disk drives. (See, for example, B. Armstrong-Hélouvry, P. Dupont, and C. Canudas de Wit, “A survey of models, analysis tools and compensation methods for control of machines with friction,” Automatica, Vol. 30, No. 7, pp. 1083-1138, 1994; D. Abramovitch, F. Wang, and G. Franklin, “Disk drive pivot nonlinearity modeling part I: frequency domain,” Proceedings of the America Control Conference, Baltimore, Md., June 1994, pp. 2600-2603; and F. Wang, T. Hust, D. Abramovitch, and G. Franklin, “Disk drive pivot nonlinearity modeling part II: time domain,” Proceedings of the America Control Conference, Baltimore, Md., June 1994, pp. 2604-2607.) It has been found that friction, which is a dynamic nonlinear function of both system velocity and system position, lowers system gain in low frequency range, and it is difficult to obtain a complete friction model due to the complexity of friction.
For a servomechanism with a positioning accuracy in the range of micrometers, friction dynamics in the pre-sliding stage cannot be neglected in control system design. Friction introduces steady state error, tracking lag, and limit cycles in a servomechanism. For a positioning servomechanism, one of the most important tasks is to decrease system steady state error to improve the positioning accuracy. However, friction prevents system positioning accuracy from further improvement as it lowers system gain in the low-frequency range.
In addition, modern servomechanisms must be designed to perform satisfactorily to increasingly stringent specifications subject to external disturbances. This is particularly true for some positioning servomechanisms, for example, small hard disk drives. Small hard disk drives are inherently designed for portable applications. In a mobile environment, the hard disk drive must tolerate much more severe external disturbances such as shock and vibration than that which is experienced in the traditional hard disk drive environment. Therefore, external disturbances, such as shock and vibration, pose another challenge for system performance improvement.
Previous Solutions
Integral Control and Observer-Based Bias Compensation
In a Proximate Time-Optimal Servomechanism (PTOS), which is widely employed in positioning servomechanisms (as described, for example, in G. F. Franklin, J. D. Powell and M. L. Workman, Digital Control of Dynamic Systems, second edition, Addison-Wesley Publishing Company, 1990), the controller is switched from a bang—bang controller to a linear PD controller when the system position error is less than a predefined threshold. As the friction limits the system gain in the low frequency range, the PTOS control cannot satisfy the requirement for high precision in some servomechanisms. To solve this problem, the most commonly used techniques are: (1) the integral control, and (2) the observer-based compensation. It is well known that integral control in the positioning system with friction leads to limit cycles. (See, for example, B. Armstrong-Hélouvry, P. Dupont, and C. Canudas de Wit, “A survey of models, analysis tools and compensation methods for control of machines with friction,” Automatica, Vol. 30, No. 7, pp. 1083-1138, 1994; and B. Armstrong and B. Amin, “PID control in the presence of static friction: a comparison of algebraic and describing function analysis,” Automatica, Vol. 32, No. 5, pp. 679-692, 1996.) The observer-based compensation is developed under the assumption that the disturbance is a constant bias such that the derivative of the disturbance with respect to time is zero, which is the basic assumption for the design of the observer. (See, for example, G. F. Franklin, J. D. Powell and M. L. Workman, Digital Control of Dynamic Systems, second edition, Addison-Wesley Publishing Company, 1990.) However, this assumption is unrealistic for friction at the micrometer level, where the friction dynamics cannot be neglected.
Measured Acceleration Feedback
Utilizing acceleration feedback to improve system performance of a servomechanism is not new. For example in hard disk drives, Sidman (U.S. Pat. No. 5,426,545), Abramovitch (U.S. Pat. No. 5,663,847) and the related references cited in their patents proposed to use accelerometers mounted on the base plates of hard disk drives, with the sensed acceleration signals used to compensate for the disturbances on Read/Write (R/W) heads. However, in these patents, the sensed acceleration signal is the acceleration of the base plate rather than that of the R/W head since it is difficult and not feasible to mount accelerometers on the R/W head. Therefore, in this scheme, the effects of external shock and vibration on the R/W head are only indirectly sensed. Furthermore, the internal nonlinear disturbances to the R/W head, such as, friction, windage and ribbon flexibility, cannot be sensed and compensated for in this scheme. Moreover, the need for accelerometers makes this scheme expensive and complicated.
Estimators-based Compensation
Another scheme to reject the low-frequency disturbances including friction in a servomechanism is based on a disturbance estimator originally proposed by K. Kaneko et al, in “High stiffness torque control for a geared dc motor based on acceleration controller,” Proceedings of IECON'91, pp. 849854. In this scheme, the low-frequency disturbances are estimated and compensated for using open-loop feedforward compensation. This method is sensitive to the accuracy and variations of the parameters in the loops because of the open-loop feedforward compensation.
In summary, there is no prior solution which can attenuate the influences of both internal disturbances such as friction and external disturbances such as shock and vibration for servomechanisms more effectively, more robustly, more simply and economically.